 Solve by Completing the Square 1. x 2 - 4x + 7 = 0 2. x 2 + 8x = 2 3. x 2 - 2x = -9 (Save room, we have a reloop warm up next!)

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 Solve by Completing the Square 1. x 2 - 4x + 7 = 0 2. x 2 + 8x = 2 3. x 2 - 2x = -9 (Save room, we have a reloop warm up next!)

1. If 3x is one factor of 3x 2 – 9x, what is the other factor? 2. When x 2 – 9 and x 2 – 5x + 6 are factored, a common factor is what? 3. Factor completely 72a 3 b 4

 A radical expression contains a square root.  A radicand, the expression under the radical sign, is in simplest form if it contains no perfect square factors other than 1.  Using prime factorization we can simplify radical expressions. Radical or Square Root  Radicand

 X 2 = ______  16 = _______  49 = _______



 Examples: 1. 2.

 Examples: 1. 2.

3. 4.



 On the half sheet… ◦ Simplify each radical, WITHOUT a calculator!  The first group done with ALL correct answers gets CANDY!

 Graphing –not always exact. need a graphing calculator to find exact values. don’t always have a solution.  Factoring – doesn’t always work. only use when factors are easy to find.  Quadratic Formula – always works and get exact values. need a 4-function calculator with a square root button to approximate.

 Pop Goes the Weasel Pop Goes the Weasel  Gilligan Gilligan  Mrs. Sawyer’s Way

 Standard Form of a Quadratic: ax 2 + bx + c = 0, where a ≠ 0. Song 1: Frere Jacque --opposite b, opposite b --plus or minus square root --b squared minus 4ac --all over 2a, all over 2a Song 2: Pop Goes the Weasel x equals negative b plus or minus the square root of b squared minus 4ac all over 2a

 Create a song or poem to help remember the Quadratic Formula. ◦ +5 points on test  Perform it for the class. ◦ +10 points ◦ extra points will be awarded for level of creativity during the performance  Due by Wednesday, March 6 th

1. Use 2 methods to solve x 2 – 2x – 24 = 0 Factoring:Quadratic Formula:

2. Use 2 methods to solve x = 18x Factoring:Quadratic Formula:

3. Solve 4x 2 – 2x = 7 Quadratic Formula:

4. Solve: 3x = -4x Quadratic Formula:

1. p 2 + 4p = t 2 + 2t – 3 = 0

 We can determine the number of “real number” solutions by looking at part of the quadratic formula.  We will only concern ourselves with the “real” solutions. You will learn about the imaginary solutions later in your math career.

 The part of the quadratic formula containing the radical is called the discriminant. Quadratic FormulaDiscriminant

1. 9x 2 – 12x + 4 = x 2 + 3x + 7 =

Workbook Page #10-28 EVEN And the ½ sheet of radicals